Integrated analytical–numerical methodology for reducing root and contact stresses in spur gears

Power transmission in mechanical systems is achieved by modifying speed and torque through gears. These gears are crucial components in various applications, including vehicle steering systems and drivetrains. Typically, gears are selected from standardized sizes available in the market. However, certain applications require gears with specific profiles to meet performance targets. To the best of the authors’ knowledge, the methodologies for designing these specialized gear profiles are limited, presenting a challenge for engineers and designers. Consequently, there is a significant need for comprehensive research and development in this area to optimize gear performance and efficiency. This study develops a framework to evaluate the stress behavior of spur gears through the integration of (i) ISO 6336 analytical evaluation, (ii) 3D finite element analysis (FEA), and (iii) statistical Design of Experiments with Response Surface Methodology (RSM). The proposed geometry–optimization methodology, guided by RSM-derived decision rules, achieved statistically validated reductions of approximately 30% in root stress and 8% in contact stress without altering load or material. Agreement between ISO 6336 analytical predictions and FEA remained within \(\pm 5\%\), confirming the reliability of the modeling approach. The resulting framework provides designers with a quantitative and interpretable map linking geometry to stress, enabling rational trade–offs between bending and contact performance in early gear design stages.